answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aliya0001 [1]
1 year ago
5

What is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the rati

o $3:4:5$?
Mathematics
2 answers:
steposvetlana [31]1 year ago
8 0

Let

3x----> angle exterior 1

4x----> angle exterior 2

5x----> angle exterior 3


we know that

The exterior angles of any polygon add up to 360 degrees

so

3x+4x+5x=360-------> 12x=360----------> x=30°


The largest of exterior angles is equal to the smallest of interior angles

so

the largest of exterior angles is 5x------> 5*30=150°

the smallest of interior angles is 180°-150°=30°


therefore


the answer is

the smallest of interior angle measure 30 degrees

SVEN [57.7K]1 year ago
6 0

Answer:

30 degrees

Step-by-step explanation:

Since the exterior angle measures have the ratio $3:4:5$, they are $3x:4x:5x$ for some value of $x$. Each exterior angle is supplementary to an interior angle, so the measures of the interior angles of the triangles are $180^\circ - 3x$, $180^\circ - 4x$, and $180^\circ - 5x$. The sum of the interior angles of a triangle equals $180^\circ$, so we have

\[(180^\circ -3x) + (180^\circ - 4x) + (180^\circ - 5x) = 180^\circ.\]Simplifying this equation gives $-12x = -360^\circ$, so $x = 30^\circ$. Therefore, the smallest interior angle has measure $180^\circ - 5x = \boxed{30^\circ}$.

You might be interested in
a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet
tangare [24]

Answer:

<em>50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.</em>

Step-by-step explanation:

Suppose, the number of Chef's salad is x and the number of Caesar salad is y

On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.

So, the two constraints are:  40\leq x\leq 60 and  35\leq y\leq 50

The total number sold has never exceed 100 salads. So, another constraint will be:   x+y\leq 100

According to the graph of the constraints, the vertices of the common shaded region are:  (40,35), (60,35), (60,40), (50,50) and (40,50)   <em>(Refer to the attached image for the graph)</em>

The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be:  P=0.75x+1.20y

For  (40, 35) ,   P=0.75(40)+1.20(35)=72

For  (60, 35) ,   P=0.75(60)+1.20(35)=87

For  (60, 40) ,   P=0.75(60)+1.20(40)=93

For  (50, 50) ,   P=0.75(50)+1.20(50)=97.5 <u><em>(Maximum)</em></u>

For  (40, 50) ,   P=0.75(40)+1.20(50)=90

Profit will be maximum when x=50 and y=50

Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

6 0
2 years ago
The New Haven High School cheerleaders got a t-shirt gun. The cheerleaders stand
nevsk [136]

Answer: the gun was held 4ft high i.e H = 4ft

Step-by-step explanation:

To determine how high the gun was held when it was fired H;

Before firing the t-shirt up, the gun and the t-shirt are both at the same height.

Therefore,

H = h(0) i.e h(t) at t = 0

h(t) = -16t^2 + 64t + 4

H = h(0) = -16(0)^2 + 64(0) + 4

H = 4ft

7 0
2 years ago
Solve for x. Round to the nearest tenth, if necessary.
ANEK [815]

Answer:

Step-by-step explanation:

take 69 degree as reference angle

using sin rule

sin 69=opposite/hypotenuse

0.93=7.2/x

x=7.2/0.93

x=7.74

x=7.7

5 0
1 year ago
Which statement justifies that 3x2 − 2x − 4 multiplied by 2x2 + x − 3 obeys the closure property of multiplication? The result 6
zalisa [80]

We have been given two polynomials 3x^2-2x -4 \text{ and } 2x^2+x-3

Let us first multiply these polynomials.

(3x^2 - 2x - 4)(2x^2 + x - 3)\\&#10;\\&#10;=3x^2(2x^2 + x - 3) -2x(2x^2 + x - 3)-4(2x^2 + x - 3)\\&#10;\\&#10;=6 x^4 - x^3 - 19 x^2 + 2 x + 12

Now, we know that polynomials follows closure property of multiplication.

It means that when we multiply two polynomials, the result will be a polynomial.

Since, when we multiplied the given polynomials, we got 6 x^4 - x^3 - 19 x^2 + 2 x + 12 which is a polynomial.

Therefore, the correct option is

The result 6 x^4 - x^3 - 19 x^2 + 2 x + 12   is a polynomial.


4 0
1 year ago
The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50
pashok25 [27]

Answer:

the answer is A

Step-by-step explanation:

edgenuity

6 0
1 year ago
Other questions:
  • joe is preparing 18 hot dogs for his party however Joe only has 12 hot dogs buns how many hot dogs buns does Joe needs
    11·2 answers
  • In a study on the fertility of married women conducted by Martin O’Connell and Carolyn C. Rogers for the Census Bureau in 1979,
    5·1 answer
  • Classify the expression: 5x + 3x2 − 7x3 + 2.
    9·2 answers
  • Consider the following hypothesis: "There is no relationship between income and amount of money spent on food." If the hypothesi
    11·1 answer
  • If Jose earns $1700 this year selling T-shirt’s he screen prints in his garage what taxes would he need to pay?
    10·2 answers
  • Will a 7/32 inch diameter pin fit into a reamed hole with a diameter of 0.215 inches?
    7·1 answer
  • A meteorologist is studying the monthly rainfall in a section of the Brazilian rainforest. She recorded the monthly rainfall, in
    11·1 answer
  • Tina is playing a computer game. She starts with 100 points, and she loses points based on the following rules: • Each time a pl
    12·2 answers
  • The Chang family is on their way home from a cross-country road trip. During the trip, the function D(t) = 2,280 - 60t can be us
    10·1 answer
  • (b) In a continuous series the average weight of some students is 75 kg and the sum of the weights is 6000 kg. Find the number o
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!